Post buckling analysis of cold rolled strip based on incompatible F?ppl-von Kármán equations
LI Nong1,LI Hong-bo1,ZHANG Jie1,JIA Sheng-hui2,CHU Yu-gang2,LIU Hai-jun2
(1. School of Mechanical Engineering,University of Science and Technology Beijing,Beijing 100083,China 2. Production Line of Tandem Cold Mill,Wuhan Iron and Steel Company Limited,Wuhan 430083,Hubei,China)
Abstract:In order to reveal the relationship between pre-buckling residual stress and post buckling deflection,post buckling residual stress of cold rolled strip,the incompatible F?ppl-von Kármán equations is introduced to establish the model of boundary value problem of nonlinear partial differential equations of infinite strip with two free boundaries. The boundary value problem of nonlinear partial differential equations is simplified to a boundary value problem of nonlinear ordinary differential equations with consideration of harmonic pattern of deflection. After non-dimensionalization of the involved quantities,the non-dimensional deflection with undetermined coefficients are determined by analyzing the magnitude of quantities. The total potential energy can be written only by using non-dimensional deflection and the undetermined coefficients are calculated by using Ritz method. The calculated deflection agrees well with results mentioned in other literature,and the deviation is explained. Aiming at a typical product of a cold rolling mill,the post buckling released residual stress is calculated and the minimum tension is determined,which provides a reference to application of flatness measurement.
李 秾,李洪波,张 杰,贾生晖,褚玉刚,刘海军. 基于非协调F?ppl-von Kármán方程组的冷轧带材后屈曲分析[J]. 钢铁, 2017, 52(5): 47-54.
LI Nong,LI Hong-bo,ZHANG Jie,JIA Sheng-hui,CHU Yu-gang,LIU Hai-jun. Post buckling analysis of cold rolled strip based on incompatible F?ppl-von Kármán equations. Iron and Steel, 2017, 52(5): 47-54.
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